(1) The sample mean stands at 1480 hours while the population standard deviation is 80 hours.(2) The null hypothesis posits that the average lifespan of fluorescent bulbs is 1500 hours.(3) The critical value is 1.645.(4) The test statistic is D, -1.58.(5) The conclusion is B, we reject H0.(6) Thus, the conclusion indicates A, there isn't sufficient evidence to substantiate the claim that the average lifespan of its fluorescent bulbs is 1500 hours.
There will still be 34.5 L of water in the two pails combined because no water is lost.
Thus the total remains 34.5 L after transferring water between them.
Let the final amount in the smaller pail be x.
Then the larger pail contains 9x.
So x + 9x = 34.5.
That simplifies to 10x = 34.5.
Dividing both sides by 10 gives x = 3.45.
Therefore the smaller pail held 3.45 L at the end.
Because 0.68 L was poured into it, its initial volume was 2.77 L (3.45 minus 0.68)
We can also deduce the larger pail initially contained 31.73 L
(either 35 minus 2.77, or 9 times 3.45 plus 0.68)
Given that,
Julia completes a 20-mile bike ride in 1.2 hours.
The distance Julia covers is 20 miles and her time taken is 1.2 hours.
Therefore, Julia's speed = 
= 16.67 mph
Katie finishes the same 20-mile ride in 1.6 hours.
Katie’s distance is 20 miles and her time is 1.6 hours.
Hence, Katie's speed = 
= 12.5 mph
To determine how much faster Julia rides compared to Katie, subtract Katie’s speed from Julia’s speed.
Thus, 16.67 mph minus 12.5 mph equals 4.17 mph, approximately 4.2 mph.
Consequently, Julia cycles 4.2 mph faster than Katie.
Response:
a) 8
b) 15
c) 34
Detailed explanation:
Section a) Options for neck-wear
Regular ties count = 3
Bow ties count = 5
Overall ties count = 3 + 5 = 8
Any tie can be selected from these 8 available options. Thus, the options for neck-wear total 8.
Section b)
We now calculate choices for using both regular and bow ties.
Selecting a regular tie is independent of the bow tie selection. According to counting principles, if two events are independent, the total ways to realize both equal the product of their individual possibilities. Thus,[
Number of ways to select both ties = Count of ways to choose each tie
So,
Ways for wearing both types of ties = 3 x 5 = 15 ways
Section c)
Count of shirts = 5
Count of skirts = 4
Count of pants = 3
Count of dresses = 7
Choice options for outfits include:
- Shirt paired with Skirt or Pants
- Or simply a dress
Pants can be chosen in 3 ways. Pairing a skirt or pant provides 9 options.
Reapplying counting rules:
Ways to wear a shirt with a skirt or pant = 3 x 9 = 27
Choices for dresses = 7
Consequently, the total is 27 + 7 = 34 outfit combinations.
